Theresa May’s new wave of grammar schools must give priority to “ordinary working class families” as much as to children from poorer families eligible for free school meals, the education secretary will say.

Justine Greening, in a speech briefed in advance, will say she wants selective education to benefit children from households with incomes of up to £33,000, moving the focus of education policy away from targeting the most disadvantaged households.

“To be clear, this isn’t about creating brand new labels for our families and our children. It isn’t about singling out some for support – whilst leaving others alone,” Greening is to say in her speech at St Mary’s University in Twickenham.

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“But we do want to start to provide a clearer analysis of the situation. Of how the children of ordinary working people are faring in our education system. And for measuring how our wider reforms can do better for these families – and so better for the country.”

“Grammars should not just be for one better-off group in society to attend. We want to see more children from disadvantaged families get into grammars – that’s vital,” Greening will say.

“But we also shouldn’t lose sight of the fact that many young people from an ordinary working class background already attend our existing grammar schools.

“And so, the new schools that we will create will support young people from every background, not the privileged few. Young people on free school meals – and those eligible for pupil premium. Young people from ordinary working families that are struggling to get by.”

Labour said Greening’s department had deliberately excluded the poorest families from her calculations to make access to grammar schools seem fairer and accused her of “fiddling the figures”.

“This is a classic case of policy-based evidence-making. If your kids get free school meals or qualify for the pupil premium, the government doesn’t think you’re an ‘ordinary working family’,” Angela Rayner, Labour’s shadow education secretary, said.

“But however they try to fiddle the figures, the facts are clear and simple. There is no evidence that new grammar schools will do anything for social mobility.

“Instead of wasting time and money on Theresa May’s pet projects, they should be solving the real problems facing our schools and keeping their promise to protect funding for every child.”

Labour said that DfE’s criteria effectively creates three categories of family – the poorest, defined by the pupil premium; the ‘ordinary working families’ which excludes the poorest but includes all other households; and then all the remaining households who have above-average income per child.

The Lib Dem leader, Tim Farron, said the government was “fiddling the figures, pure and simple, to make their case for a discredited grammar schools plan”.

Farron said that the announcement showed pupils of working families would lose out. “Rather than making every state school excellent the government want to spend more cash on another ideological experiment,” he said. “This speech is the political equivalent of a rose-tinted view of the 1950s where a few excel and millions of other young people are consigned to the scrapheap.”

Greening’s remarks in her speech make few references to the poorest pupils who are far less likely to attend grammar schools.

The criteria for ordinary working families uses a specific OECD metric that factors in number of children but excludes housing costs, which Labour said ignores factors like shortages of affordable housing.

Without housing costs included, the DfE’s consultation criteria will mean the bulk of “ordinary working families” are likely to live in suburbs or coastal towns, more likely to vote Conservative, rather than inner cities.

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But Greening will argue: “This is a government that believes that ordinary working families shouldn’t have to ‘make do’. We believe they deserve better than that. Because ordinary working families are the backbone of our economy, of our country.

“Fundamentally, children need more good schools. That will be at the heart of my forthcoming white paper: Schools That Work for Everyone – for the first time we want to properly knit together the different parts of our education system, so its constituent parts can work together to raise attainment as a whole, collectively.

“We believe that universities, independent schools, and faith schools have a role in creating better options for parents. And I believe that selection – in new, 21st century state grammar schools – will add to the options available to young people – to truly help make the most of their talents.”

Data in the consultation published by the DfE appears to show that the new class of families find it harder to access outstanding schools, with 21% of pupils from ordinary working families attending schools rated as outstanding compared to 25% of those from families with above-average income.

But the figures also show pupils in existing grammars schools are as likely to be from “ordinary working families” as children in non-selective schools.

Labour noted that selective schools remained dominated by children of the well-off: “The fact that over 50% of pupils at grammars earn above median income, compared to less than a third in all other schools, simply shows that the education secretary suggestion that selective schools do not only benefit the affluent is rather absurd.”